PSI - Issue 43

Atri Nath et al. / Procedia Structural Integrity 43 (2023) 246–251 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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initial estimates of the model parameters are next calibrated to obtain closer cyclic-plastic response under asymmetric stress-controlled cycles by using a genetic algorithm optimization technique. The optimized parameters thus obtained are then used to simulate the response of CSMs under both monotonic and different cyclic loading conditions. The accuracy of the prediction obtained by the current approach is compared with that of other reported predictions by using a modified root mean square error ( F error ) function given by : = { 1⁄ ∑ [( − )/ ] 2 =1 } 0.5 ℎ (5a) = { 1⁄ ∑ [( , − , )/ ] 2 =1 } 0.5 ℎ / 5(b) = { 1⁄ ∑ [( ∗ − ∗ )/ ∗ ] 2 =1 } 0.5 − (5c) where, n is the number of data points, and ∗ are the stress and modified ratcheting strain recorded from experiments, , and , are the experimental and simulated stress amplitude for the i th cycle , and and ∗ are the predicted stress and modified ratcheting strain using the CIKH model. The ratcheting strain data are modified by applying a 5% offset similar to the study by Nath et al. (2019a). The adopted optimization technique considerably reduces the value of F error . The comparison of the simulation obtained by using the suggested methodology with the reported response for the investigated materials is examined in the following section.

a b Figure 1 Schematic representation of a) contribution of individual backstresses based on the physical meaning of the parameters, and b) tensile half of stabilized hysteresis loop under strain-controlled cycles showing the dominance of individual backstress components in different zones 3. Results and discussions The adopted approach is applied to predict the cyclic-plastic response of two ferrous (CS1026 steel and SA333 C Mn steel) and four non-ferrous materials (viz., TA16 titanium alloy, AA 7075-T6 aluminum alloy, OFHC copper, and Zr- 4 alloy at 400°C ). The final sets of CIKH model parameters obtained by the adopted approach for the investigated materials (summarized in Table 2) are next used to simulate the behavior of the material under different loading conditions as depicted in Fig 2-4 for the different investigated materials. CS1026 (Hassan and Kyriakides, 1992) and SA333 C-Mn (Paul et al., 2010) steels considered in the study typically exhibit a BCC structure and are cyclically stable ((Nath et al., 2019a). The parameters of the CIKH model parameters summarized in Table 2 are used to simulate the stabilized hysteresis loop at 1% strain amplitude (Fig 2a) and ratcheting behavior under three different mean stresses (Fig. 2b). The accuracy of the predictions obtained using the current approach is quantitatively compared with other reported approached in Fig 2c; the adopted methodology provides better simulation for the cyclic-plastic response for CS1026 steel, substantiated by the consistent low magnitude of F error (3%) across all the loading conditions. Similar qualitative and quantitative comparisons between experimental and reported simulations have been carried out for FCC AA7075 alloy (Agius et al., 2018) and OFHC copper (Zhang and Jiang, 2008) in Fig. 3, and for HCP-structured TA16 titanium alloy(Kan et al., 2011) and Zr-4 alloys(Cheng et al., 2015) in Fig. 4. The adopted approach provides a low magnitude of the F error (<3%), for all the investigated materials under different loading condition; this illustrates the superior predictive capability of the suggested approach in comparison to existing approaches, as well as depicts the generalized nature of the adopted approach.